— Function: double gsl_sf_bessel_J0 (double x)
— Function: int gsl_sf_bessel_J0_e (double x, gsl_sf_result * result)

These routines compute the regular cylindrical Bessel function of zeroth order, J_0(x).

— Function: double gsl_sf_bessel_J1 (double x)
— Function: int gsl_sf_bessel_J1_e (double x, gsl_sf_result * result)

These routines compute the regular cylindrical Bessel function of first order, J_1(x).

— Function: double gsl_sf_bessel_Jn (int n, double x)
— Function: int gsl_sf_bessel_Jn_e (int n, double x, gsl_sf_result * result)

These routines compute the regular cylindrical Bessel function of order n, J_n(x).

— Function: int gsl_sf_bessel_Jn_array (int nmin, int nmax, double x, double result_array[])

This routine computes the values of the regular cylindrical Bessel functions J_n(x) for n from nmin to nmax inclusive, storing the results in the array result_array. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values.